The Modeling of Rare Events: from Methodology to Practice and Back Paul Embrechts Department of Mathematics Director of RiskLab, ETH Zurich Senior SFI.

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Presentation on theme: "The Modeling of Rare Events: from Methodology to Practice and Back Paul Embrechts Department of Mathematics Director of RiskLab, ETH Zurich Senior SFI."— Presentation transcript:

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The Modeling of Rare Events: from Methodology to Practice and Back Paul Embrechts Department of Mathematics Director of RiskLab, ETH Zurich Senior SFI Chair www.math.ethz.ch/~embrechts

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Summary: A bit of history A bit of theory An application Further work

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Perhaps the first: Nicolaus Bernoulli (1687 – 1759) who, in 1709, considered the actuarial problem of calculating the mean duration of life of the last survivor among n men of equal age who all die within t years. He re- duced this question to the following: n points lie at random on a straight line of length t, calculate the mean largest distance from the origin.

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Some isues: Practice is too often frequency oriented... - every so often (rare event) - return period, 1 in x-year event - Value-at-Risk (VaR) in financial RM... rather than more relevant severity orientation - what if - loss size given the occurence of a rare event - Expected Shortfall E[X I X > VaR] This is not just about theory but a RM attitude!